This quote or aphorism refers to the idea that a person with more power can determine or dictate the rules of moral/ethical behavior.
The weaker person is unable to shape the behavior of the stronger person due to the imbalance of power.
In My Side of the Mountain, Sam does eat animals, but this is the nature of living in the wild, not necessarily a commentary on the ethics of power.
I don't really see "might makes right" happening in this book. Sam doesn't go out and force his way on anyone or anything like that.
"Might is right" (or, more commonly "might makes right") means that there is no such thing as right and wrong. No actions are moral or immoral. Whoever has the power to do something has the right to do it. I just don't see that happening in this book.
Might is right basically means that the stronger one wins. In this book, the point seems to me to be to get away from our modern society and live life on your own terms. Of course, might is right can also be considered the law of nature.